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Added new lemma: mod_false_spec #202

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Merged
merged 2 commits into from
Aug 21, 2025
Merged

Added new lemma: mod_false_spec #202

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76d688d
added mod_false_spec
Shark-with-Blue-Shoes Jul 30, 2025
51bf443
rename new lemma to `testbit_false_mod_pow2`
andres-erbsen Aug 21, 2025
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7 changes: 7 additions & 0 deletions theories/Numbers/Natural/Abstract/NBits.v
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Expand Up @@ -1312,6 +1312,13 @@ Proof.
- now rewrite ones_spec_low, mod_pow2_bits_low, andb_true_r.
Qed.

Lemma testbit_false_mod_pow2 :
forall a n j, testbit a n = false -> testbit (a mod 2 ^ j) n = false.
Proof.
intros a n j H. rewrite <- land_ones. rewrite land_spec.
rewrite H. rewrite Bool.andb_false_l. reflexivity.
Qed.

Lemma land_ones_low : forall a n, log2 a < n ->
land a (ones n) == a.
Proof.
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